Is it reasonable to think that something that's "softer" than the crown (I'm assuming a SS barrel) will be able to damage it? I'm thinking about plastic bristle brushes, bronze bristle brushes, coated gun rods, etc. I CAN understand the possibility of damage if you're using a stainless UNCOATED rod. Am I not thinking about this correctly?

Interesting topic, perhaps I can muddy the waters a bit. Wear between two dissimilar metals would normally expected to sacrifice the softer of the two and often does. But not always. As an aviation accident investigator in the Army I had the unwelcome task of convincing "superior" officers that one crash caused by loss of control had in fact been caused by a .015" thick aluminum tab wearing through a 3/16" 19 strand stainless control cable after a nylon bushing had fallen free. Tough sell but an indisputible fact. Sometimes softer metal become embedded with abrasive materials and causes wear. The example above...I know what happend and am clueless as to why.
I use brushes, nylon and bronze. I use patches, and when I feel the need, JB Borecleaner. I don't at this time have rifles that shoot bugholes at 800 yards, but when the day comes I suspect it will have similar responses to fouling as my pathetic 1/2 to 3/4 MOA shooters do today. When it gets bad enough, accuracy goes south. Then I gotta do what I gotta do...regardless of who made the barrel and what kind of air they were blowing out of what hole, measured by what gauge.

There are others with the borescope/tv screen rigs that proclaim bronze bristles do harm stainless barrels and they have seen it. Look at Speedy's writings on the subject

Back to your cleaning thing. My Kreiger 30" barrel was streaking something fierce when new and Butches/JB just was not doing it.
I ran a cotton mop with 10%industrial ammonia through it and the copper was foaming BIGTIME. In 10min I had a clean barrel without any brushing at all. Now it is all I use. At $5.00/gallon I just don't get why others are not using this. One tip though. DO NOT USE THIS STUFF INDOORS.